Abstract

Several game theoretical topics require the analysis of hierarchical beliefs, particularly in incomplete information situations. For the problem of incomplete
information, Hars´anyi suggested the concept of the type space. Later Mertens & Zamir gave a construction of such a type space under topological
assumptions imposed on the parameter space. The topological assumptions
were weakened by Heifetz, and by Brandenburger & Dekel. In this paper we
show that at very natural assumptions upon the structure of the beliefs, the
universal type space does exist. We construct a universal type space, which
employs purely a measurable parameter space structure.
We divided this work into two parts. In the first part we introduce the main ideas and features of type space. We follow Heifetz & Samet, however we take some steps out of their work. We also introduce an example to present the usefulness of type space.
In the second part we present a complete universal type space, which contains the works of Mertens & Zamir, Heifetz, and Brandenburger & Dekel
as a special case. The two parts of this work can be read separately, therefore there are some minor parallelism in this paper.